8th Maths 2.6

Chapter 2

Linear Equations in One Variable

NCERT Class 8th solution of Exercise 2.1

NCERT Class 8th solution of Exercise 2.2

NCERT Class 8th solution of Exercise 2.3

NCERT Class 8th solution of Exercise 2.4

NCERT Class 8th solution of Exercise 2.5

Exercise 2.6

Solve the following equations.

Q1. `text{8x - 3}/text{3x} = 2`

`text{Sol.}`

`text{8x - 3}/text{3x} = 2`

`text{8x - 3} = text{3x} times 2`

`text{8x - 3 = 6x}`

`text{8x - 6x = 3}`

`text{2x} = 3`

`text{x} = 3/2`

`text{Answer:}`

`text{x} = 3/2`

Q2. `text{9x}/text{7 - 6x} =15`

`text{Sol.}`

`text{9x}/text{7 - 6x} = 15`

`text{9x} = 15 times text{7 - 6x}`

`text{9x = 105 - 90x}`

`text{9x + 90x} = 105`

`text{99x} = 105`

`text{x} = 105/99`

`text{x} = 35/33`

`text{Answer:}`

`text{x} = 35/33`

Q3. `text{z}/text{z + 15} = 4/9`

`text{Sol.}`

`text{z}/text{z + 15} = 4/9`

`text{9z} = 4 times text{z + 15}`

`text{9z = 4z + 60}`

`text{9z - 4z = 60}`

`text{5z} = 60`

`text{z} = 60/5`

`text{z} = 12`   

`text{Answer:}`

`text{z} =12`

Q4. `text{3y + 4}/text{2 - 6y} = -2/5`

`text{Sol.}`

`text{3y + 4}/text{2 - 6y} = -2/5`

`5times text{3y + 4} = -2times text{2 - 6y}`

`text{15y + 20 = - 4 + 12y}`

`text{15y - 12y} = -20 - 4`

`text{3y} = - 24`

`text{y} = -24/3`

`text{y} = - 8`

`text{Answer:}`

`text{y} = - 8`

Q5. `text{7y + 4}/text{y + 2} = - 4/3`

`text{Sol.}`

`text{7y + 4}/text{y + 2} = - 4/3`

`3times text{7y + 4} = - 4times text{y + 2}`

`text{21y + 12 = - 4y - 8}`

`text{21y + 4y = - 8 - 12}`

`text{25y} = - 20`

`text{y} = - 20/25`

`text{y} = - 4/5`

`text{Answer:}`

`text{y} = - 4/5`

Q6. The ages of Hari and Harry are in the ratio `5 : 7`. Four years from now the ratio of their ages will be `3 : 4`. Find their present ages.

`text{Sol.}`

`text{Let  Hari's present age 5x years}`

`text{and Harry's present age 7x years}`

`text{After 4 years Hari's age (5x + 4) years}` 

`text{After 4 years Harry's age (7x + 4) years}`

`text{According to question}`

`text{(5x + 4)}/text{(7x + 4)} = 3/4`

`4times text{(5x + 4)} = 3times text{(7x + 4)}`

`text{20x + 16 = 21x + 12}`

`text{20x - 21x = 12 - 16}`

`text{- x} = - 4`

`text{x} = 4`

`text{Hari} = 5 times 4 = 20`

`text{Harry} = 7 times 4 = 28` 

`text{Answer:}`

`text{Hari's present age 20 years and}`

`text{Harry's present age 28 years}`.

Q7. The denominator of a rational number is greater than its numerator by `8`. If the numerator is increased by `17` and the denominator is decreased by `1`, the number obtained is `3/2`. Find the rational number.

`text{Sol.}`

`text{Let numerator be x}`

`text{and denominator be (x+8)}`

`text{According to question}`

`text{x + 17}/text{(x + 8) - 1} = 3/2`

`2times text{x + 17} = 3 times text{x + 7}`

`text{2x + 34 = 3x + 21}`

`text{2x - 3x = 21 - 34}`

`text{- x} = - 13`

`text{x} = 13`

`text{dnominator = 13 + 8 = 21}` 

`text{Answer:}`

`text{Rational number is } 13/21.`